The Ba'ku claim predates the existence of the federation by a century ...
At no point in the movie did the Baku ever claim the planet, or express anything verbally that could be taken as indicating they feel they "owned" it.
They referred to it as their home many times.
They were living there as the sole occupants for a significant period of time (nothing specific, but seemlingly hundreds of years).
To whom would they file their claim? Does the Federation or Starfleet, or whatever empire etc., around have a formal system of some kind?